Theorem[4.1.10] Let X and Y be a topological spaces and assume that A C X and BCY. Then the topology on A × B as a subspace of the product X × Y is the same as the product topology on A × B, where A has the subspace topology inherited from X, and B has the subspace topology inherited from Y. Proof: H.W Theorem [4.1.11]

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

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Q: 15. Let V be the set of those polynomials ax² + bx + c € P₂ such that P2 a + b + c = 0. Is V a…

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A: Given:V is a vector space with subspaces U and W. To Prove:U∩W is a subspace of V.

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A: Note: As per our guidelines, we can solve first three subparts. Please repost remaining part…

Q: f) V = R³; W = {(a, b, c) e IR³ |3a + 2b − c = 0} g) V = {ax² + bx + c a, b et c = R}; {ax² + bx +…

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Q: Let W be a subspace of R" and suppose that there is a vector v in R" with v = Projwv, then which of…

A: Let us solve above.

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Q: 6. Let V be a vector space with subspaces U and W. Show that the set UnW = {x|x EU and xEW} is a…

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Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.